article · Processes
Mathematical modelling plays a central role in tracking epidemics and managing industrial and biological processes. A new statistical model, termed the unit exponential Pareto distribution, provides a continuous three-parameter framework capable of capturing decreasing, symmetric, and asymmetric data patterns with a monotone failure rate. The distribution was evaluated using real-world data, specifically the recovery rates of COVID-19 patients in Turkey and France, alongside datasets concerning agricultural milk production and mechanical component failure rates. Key mathematical properties such as moments, entropy measures, quantile functions, and stochastic ordering were formally analysed. In performance comparisons against existing unit-based distributions, the model demonstrated superior fitting ability. Furthermore, parameter estimation showed that a Bayesian approach outperformed classical estimation techniques by delivering lower bias, reduced average squared errors, and narrower confidence intervals.
Accurate statistical models help researchers and planners understand complex real-world trends, from public health recovery rates to industrial reliability. By offering greater flexibility and precision than existing unit distributions, this model allows analysts to extract more reliable insights from bounded datasets, supporting better evidence-based forecasting and decision-making during health crises and across technical operations.
The model could enable enhanced predictive tools within statistical software for epidemiology, industrial quality control, and agricultural monitoring. Potential users include public health analysts, data scientists, and reliability engineers. At present, the work represents early-stage applied research that has been tested on retrospective datasets and simulated scenarios, requiring implementation into commercial statistical libraries before it can be used in industry workflows.
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In 2019, a new lethal and mutant virus (COVID-19) spread around the world, causing the deaths of millions of people. COVID-19 demonstrates that scientists are involved in significant research efforts to face bacteria with less effort than that dedicated to viruses. Since then, engineers and bio-materials scientists have been trying to develop antiviral research and find a suitable effective medication. Strategies and opportunities for interference diagnostics, treatment strategies, and predicting future factors became mandatory. From a statistical point of view, estimating and modelling these factors play an important role in preventing future viral epidemics. In this article, modelling the recovery rate of COVID-19 is investigated through a new distribution which is called the unit exponential Pareto distribution. The new continuous distribution with three parameters displays a prominent level of flexibility to model decreasing, symmetric, and asymmetric data with a monotone failure rate. The recovery rates of COVID-19 in Turkey and France were examined; moreover, milk production data and components’ failure rates are presented for data modeling. The obtained results proved the superiority of the newly suggested model compared to other unit-based distributions. Several statistical features are studied such as the quantile function, the moments, the moment-generating function, some entropy measures, the ordered statistics, the stress–strength, and stochastic ordering. Two classical estimation methods are used in addition to the Bayesian method. The statistical features and estimation analysis are evaluated using numerical and simulation techniques. As a result, we obtain the efficiency of using the Bayesian method over the classical ones, with respect to the bias, average squared error, and the length of confidence intervals for the unknown parameters.
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DOI: 10.3390/pr11010232
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